Re-conceptualizing Zero; or: Zero-stroke

Tonight, I want to talk about zero (big props to Petra for the music).  To be honest, I’ve resisted the exploration of zero for some time, despite it being part of the name of this blog collective, a collective which agrees so much on the challenges of thinking through a post-nihil praxis from the side of philosophy or conceptualization (albeit in different ways).

There always seemed to be something quite off-putting about zero…perhaps it was the way it came off as a nihilistic impulse, a desire for the minimization of “the human” or of “life,” for wearily evacuating the ontological “fullness” of substance via a contractive immunological shrinking of subjects in bewildering pain.  Plus, there were all these terms and concepts more or less proximately attached to zero that I struggled to take seriously: non-beingvoid, holeemptinesslackkenosisnothingnessnegation negativity…you get the idea.  With my spinozist training, it made absolutely no sense to use these words and concepts to talk about actually extant individuals / things / beings / objects / relations (pick your poison), etc.  With a reality immanent only to itself, fuelled by a principle of sufficient reason that emphasizes causality for the existence of things, Spinoza’s substance–and its philosophical heirs, like Deleuze’s “pure difference”–allows for no vacuum, no place or space devoid of the necessity of communicative relation, since everything that can exist, does exist, and only exists by its relations with other existing things–the abolishment of ciphers of non-being (including “possibility” as mere phantasmic projection of the present).

From the psychotic standpoint of substance, none of these terms could have legitimate meaning, with the subsequent corollary that if we were to talk about these things or concepts, it could only be as spinozistic “inadequate ideas.”  By inadequate ideas, I mean ideas (could be “minds,” “cognition,” “mental states,” “experience,” etc.) that express some degree of existence, some degree of power, by which all things come to be and strive to continue being until acted upon destructively by its relations with other things–and in this sense, they are “true” by the sheer force of their positive existence–, but simultaneously ideas that inadequately know the causal relations involved in producing said positivity, said “is-ness” of their existence.  Inadequate representational mapping of “what is the case,” attempts to conceptualize the excess of infinitude with strange theological themes.  [Example: thinking that human sacrifice will produce the continuation of the sun or cosmos rather than the gravitational orbiting of the heliocentric model; thinking that the market is a natural process rather than an historic episode of economic production that is by no means essentially “natural”]  In other words, a language of negativity that is constitutively unable to see how its referents could only be things that exist, and not what is not, not some exceptional spinozistic “kingdom within a kingdom” that would be exempt from the deterministic necessity of natural or physical laws that all things share and abide by.  No naturalist “being” here and then a non-naturalist puncture “hole” or dash of “non-being” over there.

Given this logic of the impossibility of a “kingdom within a kingdom”–which I continue to commit to for this elaboration, as it remains a necessary part of a conceptualization that is committed to naturalism and materialism–I take these terms to be indicative or expressive of conceptual territories or “intensities,” “mental” effects that have undergone some sort of codification as subjective experience.  They name modalities of what it is possible to think, regardless of whether they are fit for a rigorous naturalist-materialist metaphysics or aiding thought’s capacities for more adequate representation or not.  They are concepts related to other concepts and semantic usages, providing a resonance or support by which certain possibilities of thought are explored.  Or perhaps they are more like Negarestanian elements of unfolding programs, philosophy as space of conceptual functions, operational effects, specific sets of realizabilities, and experimentations–the practice of philosophy as elaboration itself not an immune “kingdom within a kingdom,” but always inserted and realized in media res with its time, its ecologies, and their problems.


But zero is different.  Zero is not just another conceptualization that overdoses on the symbolic register of subjective experience, although we admit that it can have a metaphorical dimension too.  Nor is zero its clumsy cousins groping around awkwardly for the metaphysical light switch.  Instead, zero has a mathematical rigor to it that exceeds the others, a reality proper that would be real regardless of whether there were beings to know it such that it would then become real.  Zero is not dependent on experience, although experience involves “it” and (as I later hope to show) implicates it, and explicates it.  We see that there must be a positivity to zero as something that is real, as something that belongs to the ineliminable mathematical structuration of our universe–“absence” or “non-being” won’t do.

But how are we to think zero in its positivity, its is-ness, when it is so commonly used to denote empirical absence or nothing?  If “Being is said in a single and same sense of everything of which it is said,” (univocity from Deleuze’s D&R, 36) and zero as real cannot be the “opting” out of reality that its associations with nothingness would take it to be, then what can we say about zero’s actuality?  Here we will look to the mathematician Gottlob Frege to give us a boost.  As Levi points out in a somewhat recent blog post on zero, Frege in his Foundations of Arithmetic says that “Zero is the number non-identical to itself.”  Frege recognizes the is-ness of the positivity that is zero.  Yet how are we to understand zero given the instability of its being non-identical to itself?  How does zero not suddenly transform into another number, a non-zero numeral?



To enter the space of the problem of reflexive non-identity, or a self-non-coincidence, I think that certain elements of Deleuze’s conceptualizations of a non-empirical (i.e. not a difference between things) difference can help.  For the basis of his ontology, Deleuze puts forth a Bergsonian concept of difference that is not subordinated to identity, analogy, opposition, or resemblance.  Such difference is the fullness of reality not as the collectivity of things that exist to compose a super-thing or super-object (an object having a discernible identity), but as a process which overwhelms the specificity of any given identity or thing used to nominate or demarcate the entirety of reality.  Following Heidegger, Deleuze is working under the framework that Being is not a being (“ontological difference”), that a sort of “pure” difference that produces such identities or objects is not reducible to them or to what is proper to them.  Given the spatio-temporal (and perhaps other, unknown dimensions) complexity and scale of the universe, and our (relatively speaking) paucity of knowledge and experience of it, this shouldn’t be much of a surprise.

What is key to this concept of difference that I would like to tease out is the way that it is a difference that differs from itself as a temporal–or perhaps better, temporalizing–process.  Instead of being self-identical such that A = A, Deleuze conceives of difference as time itself, what he calls the “pure and empty form of time” (following Kant’s phrasing).  Just as the second law of thermodynamics stipulates that there is a time-asymmetry of entropy such that time is irreversible, so we can understand Deleuze’s temporalizing difference as incapable of “returning” to a particular “distribution” of reality.  Deleuze’s difference can never “coincide” with what it “was” at some point, it can never be equal or commensurable to itself as A = A suggests.  The transformations of such difference irrevocably changes what it is, as time “goes on” and entropy increases.  These transformations require that difference be a process (e.g. time) irreducible to the simplicity of a logical identity, to being a logical term that could be equated to another.  If we are to take seriously this concept of difference, one that resists exhaustive identities that attempt to circumscribe its novelties and capacities and possibilities, then we can make the skip and a hop to see how such difference is non-identical to itself…not because it shares no relationship with identities, but because identities (and the analogies, resemblances, and oppositions that are premised on them) are inadequate for thinking the “fullness” of such difference as the unfolding production of time.

By placing such difference as the genetic element whereby all is and was and comes to be (the fullness of time), we enter into a conceptual space that can think this processual difference as a process of production that is its becoming non-identical to itself.  And here’s where we explicitly return to zero.  Although we don’t want to limit zero to the side of subjectivity, to experience, this path can be helpful for elucidating how we could more adequately understand zero.  In Deleuze & Guattari’s A Thousand Plateaus, we find an interesting conceptualization of zero, specifically in their “How do you make yourself a body without organs?” chapter / plateau.  Their concept of the Body without Organs (BwO) is a reformulation of certain elements of Kant’s theory of subjectivity as found in his critical project.  Like Kant, D&G focus upon an experiential subjectivity, both from and on the side of experience.  Specifically, they target desire: “The BwO is desire; it is that which one desires and by which one desires.”  This echoes Kant, who suggests that the faculty (or capacity or power) of desire is the “faculty which, by means of its representations, is the cause of the actuality of the objects of those  representations.”  Both concepts of desire are crucial for evincing the productive activity constitutively involved in experience, thought as a dynamic process; furthermore, production in both cases refers to the intensive dimension of experience, an intensive dimension that is foundationally related to what both authors term “= 0.”

As D&G helpfully suggest, this intensive quantity can be understood better if we conceptualize the BwO as “matter that occupies space to a given degree–to the degree corresponding to the intensities produced” by desire.  All of experience in its pure positivity of being is a modulating occupation of space such that all features of experience and experience-as-process are to be indexed “between 0 and a” (Kant).  The qualitative intensities [gradiations of color, of emotions or moods, of all sorts of specific identities that we can recognize as such within experience] populating the BwO/s, or one’s desire/s, correspond to quantitative “degrees” of reality, to fullnesses of “occupation” of matter.  Kant’s suggestive degree “a” is a placeholder or variable for any possible degree, any sort of qualitative-quantitative intensity.  The intensive degrees of consciousness are in flux, never remaining the exact same, undergoing continual metamorphoses along a quantitative gradient as continuous becoming…but what it cannot ever be is the = 0 that it is always positively in relation to.

But what is this degree zero, and why is it specifically zero?  D&G give us hints: “Matter equals energy.  Production of the real as an intensive magnitude starting at zero”–“zero intensities as matrices of production”–“infinite zero” (borrowing from Artaud)–and “zero intensity as principle of production.”  From the Kantian-Deleuzoguattarian perspective of consciousness, it is impossible to experience this degree zero, since experience constitutively depends upon quantitative degrees corresponding to the positivity of experiential qualitative intensities.  That’s just what experience is, and it couldn’t be otherwise for them.  Clearly, degree zero is other than cognition, and cannot be experienced as such.  Nick Land follows this logic all the way by interlacing = 0 with death, the obliteration of experience and the cohesion it relies upon, the being “returned” to the inhuman thermodynamic flows “from whence we came”: “pure” process.

But we can take another approach.  The movement towards = 0 is a movement towards the effacement of the operational primacy of identity (which includes resemblance, opposition, and analogy) we depend upon for living, the erasure of discrete or particular differences that help constitute (recognizable or nominable) elements of our identity such that we can navigate and traverse the world.  For D&G, the rush towards degree zero is the experiencing of the increasing incoherence of non-identity as subjectivity dissolves under the pressures of an excess which it cannot absorb without radical destabilization.  Far from being “non-being,” the hybrid Kant-D&G monster takes zero as the plenum w/o remainder, what the excess overwhelming subjectivity can only intuit by undergoing the same destabilization shared by all beings (or objects or identities) as they are produced by a “pure” difference differing from itself.  Meltdown or de-nuding as philosophical method.  The horror or joy or pain or numbness–depends upon the day of the week, really–associated with finding oneself non-coinciding with…oneself.  Or better put: experiencing the inadequacy of one’s self-conceptions or modelling processes (“ego/s”) or identities to know one’s own ontological status as teeming multiplicity, or what I called in my thesis one’s alienicity or alien constitution resulting from the “wild physics” of spinozistic substance.

Zero comes to be conceptualized as the process of reflexive non-identity, the logically anterior matrix “prior” to the actual production of empirical differences between produced identities (including other numbers).  Zero is that which produces the transformative production (e.g. change) that we are acquainted with and see every day, and such production throughly depends upon zero.  Here we have come full circle: zero as that which differs from itself, as that which produces identity (and is thus related to it) without being reducible to identity (including sets or distributions of identities).  Zero as no-thing, yet related to all things.


But I find myself dissatisfied with the deleuzoguattarian conceptualization of zero, specifically with its particular anchoring within subjective experience–a residual idealism still haunts their work, which can be seen by their love of (bergsonian?) intuitive intensity as philosophical method.  They still cannot think zero more widely beyond such an experiential method.  They truncate zero, effecting an attempted taming of zero precisely at the point where they would like to re-connect with its expanse via zero’s univocity thought as self-differentiating time.  They mis-take the intensive intuition of self-non-identity–a particular, finite effect within their “general economy” of temporal difference–as more “truly” indicative of what is supposedly authentically universal:–they take the subjective experience of a destabilizing overwhelming of one’s identity as intimate entry or approximation to the “authentic” destabilization of temporal difference that is present everywhere (univocity).  The experiential knowledge proper to one’s “ongoing non-coincidence with itself” (from my thesis, as “becoming-x“) becomes a privileged indication of the process of the processual “whole,” of what transversally traverses the “One-All” of pure difference differing from itself.

But as Brassier makes clear (quoting Badiou) in his “Stellar Void or Cosmic Animal?: Badiou and Deleuze on the Dice Throw,” we have to interrogate “the possibility that Being be thought as All.”  What D&G (unwittingly?) end up doing by correlating = 0 and intensity (from the perspective of a schizophrenic phenomenology) is buying into the logic of analogy or resemblance that Deleuze in D&R suggests is wholly inadequate for more adequately thinking pure difference totally “anterior” to any identity.  By suggesting that one most faithfully approximates non-identity by moving in the direction of an intensive and destabilizing = 0–towards the wilderness of the incoherence of excess–, D&G end up becoming ensnared in a logic that projects the experienced incoherence of destabilization of identity as what is shared by all else–a heft claim that they more presume than explain.  We get here a form of pan-psychism that illegitimately extrapolates the intensive feature of human cognition–a consciousness which is only a spinozistic finite mode–as that which is necessarily shared by all…all things participating in intensive “occupations” of matter such that our experience is taken as the model from which to move around.  D&G suppose that the degree zero “underlying” all such intensities is a “deterritorializing” incoherence universally proper to ALL that is, to all that share in zero’s process of non-identity with itself.  There is a gnostic element here that supposedly “gets at” a “secret truth” of reality, effectuated by an illegitimate operation of hypostatization of one modality of experience to gain the effect of a religious intimacy with what is “sub-personal,” of what is humming “below” all forms of identity.  This amounts to a projection of finitude upon the infinite, a suggestion that what is infinite (the “infinite zero”) is more like what happens in schizophrenic phenomenology, only to the nth degree and much more chaotically.

By exporting a feature of consciousness’ finitude, D&G fail to account, ironically enough, for the fullness of the non-identity of zero, for how zero is just as much at work in coherence as it is in incoherence, in “stratification” as well as “deterritorialization.”  For D&G, process is processed by consciousness through the imprisoning prism of the lived image of the “flow.”  Although the flow indicates something about the process of zero’s non-identity, it is part of a rationally unjustifiable “philosophical decision” that is still tied to an image of things-as-processes and the dynamics proper to them.  The “flow” becomes the model for thinking process.  But as we’ve said, zero “is” the self-differentiation of non-identity–it is not a thing, even if a supermassive collection of things.  We must take the image of the flow to be something like a heuristic, and not what can then be adequate to think infinite difference (although it is still quite useful to think actual production).  I take this to be what Brassier-Badiou are pushing when they suggest that Being cannot be thought of as All, since such an All is still dependent upon operations of shared resemblance or analogy for D&G.  To state it otherwise, there is a confusion between identity as essentially processual (the becoming-x of each extant thing) and process as non-identity, as resistant or indifferent to whatever concepts or affects we use to “approximate” it (which is really, then, not an approximation).  While D&G investigate how identity incorporates zero’s processual self-differentiation, they can only do so by correlating such difference to their schizophrenic phenomenology–but the problem is that even in the experience of such an excess of the process of zero’s self-differentiation, such an excess cannot be said to “have” or “be” the character as it is sometimes experienced as one modality of thought amongst many.  For the excess is always already there, regardless of whether one is moving “towards” or “away” from degree zero.  By privileging a particular phenomenological knowledge of zero, D&G narrow zero’s process and what it is capable of other than as finite experienced excess.  Any experience of All only winds up being a fantasy.  D&G can’t deliver on the kind of difference that Deleuze was carefully trying to construct earlier in his career.

I think this is why Badiou is so often presented as something of an ontological corrective to Deleuze’s (or D&G’s) thought.  Although I have only read his Ethics (which I find to be excellent), from what I understand about his attempt to make ontology mathematics, we have an attempt to untangle the correlation between thought and being that D&G can’t quite get out of.  Badiou’s set-theoretical conceptualization of the infinite zero as “void” aims to preserve the dimension of zero that is concretely quantifiable, but not amenable to the unjustifiable intuitive or intensive methods that imprison zero within the conceptual expansiveness of the “All,” or the “One-All.”  It’s like Badiou is saying: “Alright Deleuze, you can have univocity…but you cannot accomplish it with your all-too-phenomenological, all-too-human explorations.  You narrow the infinite.  Your Kantian-Bergsonian idealist residue betrays the infinite.  You really cannot think more adequately what you earlier called the empty form of time.  You cannot truly think the inhuman.”  It is why he focuses upon the discontinuity or disruption that zero brings about…an excess not of overwhelming intuitive experience, but of that which unpredictably strikes to problematize what we take to be All or Being.  The puncture of the state of our knowledge that indicates its incompleteness, its incompleteness for truly thinking any kind of “All.”  The injection of the non-conceptualizable zero that avoids the complacency of intimacy via the method of intense or intensive experience as sufficient for one’s relation to the infinite.  Not to “know” the zero only in intensive intimacy, but in other possibilities.

In posts that will follow in the near-future, I will focus on the ethical dimensions of zero, and how to think the ethical response to zero differently from the deleuzoguattarian ethic of inhabiting the excess of zero…how to produce a different set of ethical effects by re-conceptualizing zero, while taking my ontological critique of deleuzoguattarian excessive zero seriously.

4 responses to “Re-conceptualizing Zero; or: Zero-stroke

  1. never really gave “zero” much thought in reference to the name M. gave us here beyond it having a sort of W.Gibson cyberpunkish resonance and some associations with Nil.
    does anyone know where (if memory almost serves) Lingis rightly notes that we don’t suffer from lacks but rather from abundances (ie don’t suffer from lack of food but with symptoms of hunger, etc)?
    anyway looking forward to see what you make of ethics in such circumstances, seems to be timely in our small loop of the intertubes:

  2. Pingback: Zero’s Non-identity and the Commodification of Identity-Formation; or: Sketches for a Subtractive Ethics of Zero | synthetic zero·

  3. Pingback: Notes on Guy Debord’s Society of the Spectacle | surface effects·

  4. Pingback: Production, Circulation, and Consumption of Alienation; or: Some Notes on Debord’s Society of the Spectacle | synthetic zero·

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